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 A078910 Let r+i*s be the sum of the distinct first-quadrant Gaussian integers dividing n; sequence gives r values. 6
 1, 4, 4, 10, 9, 16, 8, 22, 13, 37, 12, 40, 19, 32, 36, 46, 23, 52, 20, 93, 32, 48, 24, 88, 56, 77, 40, 80, 37, 148, 32, 94, 48, 95, 72, 130, 45, 80, 76, 205, 51, 128, 44, 120, 117, 96, 48, 184, 57, 231, 92, 193, 63, 160, 108, 176, 80, 151, 60, 372, 73, 128, 104, 190, 176 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A Gaussian integer z = x+iy is in the first quadrant if x > 0, y >= 0. Just one of the 4 associates z, -z, i*z, -i*z is in the first quadrant. a(n) = A078911(n)+A000203(n). - Vladeta Jovovic, Jan 11 2003 LINKS M. F. Hasler, Table of n, a(n) for n = 1..1000. EXAMPLE The distinct first-quadrant divisors of 4 are 1, 1+i, 2, 2+2*i, 4, with sum 10+3*i, so a(4) = 10. MATHEMATICA Table[Re[Plus@@Divisors[n, GaussianIntegers -> True]], {n, 65}] (* Alonso del Arte, Jan 24 2012 *) PROG (PARI) A078910(n, S=[])=sigma(n)+sumdiv(n*I, d, if(real(d)&imag(d)&!setsearch(S, d=vecsort(abs([real(d), imag(d)]))), S=setunion(S, [d]); (d[1]+d[2])>>(d[1]==d[2]))) - M. F. Hasler, Nov 22 2007 CROSSREFS Cf. A078911, A078458, A078908, A078909, A078930. Cf. A062327 for the number of first quadrant divisors of n. Sequence in context: A319056 A050348 A134637 * A196051 A140234 A220044 Adjacent sequences:  A078907 A078908 A078909 * A078911 A078912 A078913 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Jan 11 2003 EXTENSIONS More terms from Vladeta Jovovic, Jan 11 2003 STATUS approved

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Last modified August 11 15:12 EDT 2020. Contains 336428 sequences. (Running on oeis4.)